port from two auto plants to three dealerships Figure 1. Auto trans Question 3.

Question

port from two auto plants to three dealerships Figure 1. Auto trans Question 3. LP problem formulation-Bus Scheduling A bus company is planning to introduce a bus service to one City. The buses will operate on a 24-hour schedule starting at 00:00 and ending at 24:00. It has been decided also that each shift can start at every below: four-hour time intervals (e.g. 00:00, 4:00, 8:00 etc.). The demand for buses are is depicted in Table 2 Table 2. Bus demand per four-hour time period Time interval Bus demand 00:00-4:0 4:00-8:00 8:00- 12:00 12:00 16:00 16:00-20:00 20:00-24:00 4 8 10 7 12 4 Each shift is required to work 8-hours, based on the starting times above (e.g. a bus can start at 4:00 and end at 12:00, a bus can start at 8:00 and end at 16:00). The company wants to minimize the number of buses to operate under these rules on a daily basis t up the problem as an LP. Define variables, objective function and constraints.

Explanation / Answer

Variables :

x1 - Number of buses starting at 00:00 hrs

x2 - Number of buses starting at 04:00 hrs

x3 - Number of buses starting at 08:00 hrs

x4 - Number of buses starting at 12:00 hrs

x5 - Number of buses starting at 16:00 hrs

x6 - Number of buses starting at 20:00 hrs

Constraints - Based on demand

x1 + x6  >= 4

x1 + x2 >=8

x2 + x3 >= 10

x3 + x4 >= 7

x4 + x5 >= 12

x5 + x6 >= 4

Objective - To minimise the number of buses

Minimise x1 + x2 + x3 + x4 + x5 + x6

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